De partitiefunctie van Rademacher

Bachelor Thesis (2018)
Authors

R.M. Ros (TU Delft - Electrical Engineering, Mathematics and Computer Science)

Supervisors

J.G. Bosman ()

Faculty
Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science
Copyright
© 2018 Robin Ros
More Info
expand_more
Publication Year
2018
Language
Dutch
Copyright
© 2018 Robin Ros
Graduation Date
09-07-2018
Awarding Institution
Delft University of Technology
Faculty
Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science
Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Abstract

There are several ways to write the number 5 as a sum of positive integers, disregarding order. A quick calculation shows that this can be done in 7 ways: 5 = 5, 5 = 4 + 1, 5 = 3 + 2, 5 = 3 + 1 + 1, 5 = 2 + 2 + 1, 5 = 2 + 1 + 1 + 1 and 5 = 1 + 1 + 1 + 1 + 1. In the same way, we can count the number of ways for each integer n. Although this calculation is trivial, a closed form for this function is not as easily obtained as one for combinations, for example. This work formulates and proves Rademacher's formula for these partition numbers. It also tries to uncover some key ideas behind the proof, the supporting theory and other inspirations.

Files

License info not available